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Recenly, Harge academe medcal cenler determincd that 8 0f 18 employees in a particular posibon were female, #hereas 51% of the employees for Ihis position , Ine gen...

Question

Recenly, Harge academe medcal cenler determincd that 8 0f 18 employees in a particular posibon were female, #hereas 51% of the employees for Ihis position , Ine general workforce signifcance, there enidence Ihai the proportion Kemales Position atihis medical center dncien from Ahal wculd expected in Ite general corktorce? What are the correct hypotheses Jestlo determing Ihe proporion is different?female AfIne 0 05 le,el cHo 17051,H 1=051 0 B Ho K2051,H,I>051 0 *051,H, *+051 0 D Hc 12051 H *&l

Recenly, Harge academe medcal cenler determincd that 8 0f 18 employees in a particular posibon were female, #hereas 51% of the employees for Ihis position , Ine general workforce signifcance, there enidence Ihai the proportion Kemales Position atihis medical center dncien from Ahal wculd expected in Ite general corktorce? What are the correct hypotheses Jestlo determing Ihe proporion is different? female AfIne 0 05 le,el c Ho 17051,H 1=051 0 B Ho K2051,H,I>051 0 *051,H, *+051 0 D Hc 12051 H *<051 Caculalo tha {esi stabsbc Zsta--Dype incori oecim Aound [o ot plact3 nedoed ) Knatts tne P-va ue? The p-value niedet Ortt Round Tnies Jef mz Naces (T,pe . Slte [ne €otEiuson Jinei needad ) Aendenif conciude that tht prceaon 6f females Ehy Boalot Ints Medica caneem dillutentnorm Ene Dcconon penoral Acutorce Ht hpoihes s Tnere- Jnsaneani Clato seieci i cul anstets] Efcent



Answers

Use the data in CPS91 for this exercise. These data are for married women, where we also have infor-
mation on each husband's income and demographics.
(i) What fraction of the women report being in the labor force?
(ii) Using only the data for working women-you have no choice- estimate the wage equation
$\log (w a g e)=\beta_{0}+\beta_{1} e d u c+\beta_{2} e x p e r+\beta_{3} e x p e r^{2}+\beta_{4} b l a c k+\beta_{5} h i s p a n i c+u$ by ordinary least squares. Report the results in the usual form. Do there appear to be significant wage differences by race and ethnicity?
(iii) Estimate a probit model for inlf that includes the explanatory variables in the wage equation
from part (ii) as well as nwifeinc and kidlt6. Do these last two variables have coefficients of the
expected sign? Are they statistically significant?
(iv) Explain why, for the purposes of testing and, possibly, correcting the wage equation for
selection into the workforce, it is important for nwifeinc and kidlt6 to help explain inlf. What
must you assume about nwifeinc and kidlt6 in the wage equation?
(v) Compute the inverse Mills ratio (for each observation) and add it as an additional regressor to
the wage equation from part (ii). What is its two-sided $p$ -value? Do you think this is particularly
small with $3,286$ observations?
(vi) Does adding the inverse Mills ratio change the coefficients in the wage regression in important
ways? Explain.

Ours blanc. The fraction of women in the workforce is 3000 286, Divided by 5000 634. And we get .583. So about 60 or two. This is the old L. S. Result. We have education, we've an estimate of point 099 This one is very significant. The same to experience and experience square. Their estimates are 0.2 and minus point 0003 respectively. For black and hispanic dummy. Yes these variables have interesting signs but the estimates are not statistically significant. As you can tell that as you can tell from the fact that the standard errors are larger than the absolute values of the estimates. Yeah. So we have little evidence for differences in which by race and ethnicity. Once education and experience have been controlled for R. Three. If we include and wife, I am see And it l. T. six into the regression equation we will find their coefficient to be -1091 and minus point five respectively. Her T statistics are -13.47 and -11.5 respectively. So the effects of these factor are significant and the signs are as we expected, we expect both estimates to be negative because a woman is less likely to work. If her spouse earns more or if she has a young child in the family, March four, we must assume that controlling for education experience and race, ethnicity variables are the income and the presence of young Children do not affect which we need at least one variable to affect labor force participation. That does not have a direct effect on the wage offer. So we made this assumption. However, this assumption might be false. If employers discriminate against women who have young Children or whose husbands work March five, we calculate the mills ratio and we find the T statistic of it to be one point 77 With the p value of one oh eight, We have over 3000 observations. So this is not a very small P value. We don't have a strong evidence against the null hypothesis of no selection bias. When we add the muse ratio to the rig question, you find that the slope coefficients did not change much. The largest change happened in the intercept, but it's hard to interpret the change and it's not too important in general.

So here we have a company that employs both men and women and it's secretarial and executive positions. And in reports filed with the government, the company shows that the percentage of female employees who received raises is higher than the percentage of male employees who received raises. And a government investigator claims that the percentage of male secretaries who received raises is higher than the percentage of female secretaries who received raises, and that the percentage of male executives who received raises is higher than the percentage of female executives who get raises. And is this possible? So a no. Either the company report is wrong or the investigators claim is wrong? Be no. If the company report is correct, either a greater percentage of female secretaries than a male secretaries received raises or a greater percentage of female executives in a male executives received raises. See no. If the investigator is correct, by summation of the corresponding numbers, the total percentage of male employees who received raises would have to be greater than the total percentage of females who get raises. The all of the above were true or it's possible for both. The company report to be true and the investigators claim to be correct. So here it's actually the answer. E And that's because it's possible for both to be correct. For example, if there were 11 secretaries and say 10 were women and three got a raise, and then we had one man and one race for a man, And then we had 11 execs 10 men, one got a raise And one woman who did not get a raise. Then 100 of the male secretaries received raises While only 30 of the female secretaries do. And in this case 10 of the male executives were Subaru's, But zero of the female executives would receive a raise. However, overall three out of 11 women received raises. We're only two out of 11 men received raises. So this would be an example of Simpson's paradox and uh you know, this is why I. E. Is correct, where it's possible for both the company report to be true and the investigators claim to be correct. It's all a breakdown of the genders between the secretaries and executives.

Given the following data set, the first thing that we need to do is come up with a scatter diagram. I did this and excel, and with this we get the following plot. So what we need to do with this has come up with a label to describe the relationship between the two variables and on the horizontal access we have the percent of, um, working and on the why we have the percent of management. And because we see that as the percent of working increases, um, our percent of management increases. You can say that there is a positive relationship and because our if we draw we drew a line of best fit through this and you had a better artist, you could see that the relationship between these two variables is linear. So what that means is, as our X variable increases or by why variable increases at a constant rate. So this would be a positive linear relationship. And now with this, we have to come up with a on estimated regression equation. So in order to come up with their estimated rigor regression equation, we will use this formula. So beta subzero zehr Arab on, beta. Someone is our, um our model, basically. And in order to find these variables, we need to use the following formula. So beta sub one is equal to the sum of each individual X value of minus the mean of the excess times each individual. Why value minus the mean of the wise over some of the differences between the X variable squared. So let's come up with these values. So first thing when you do is come up with X bar. An expert is just the the average of these values up here. So 67 plus 45 plus 73 plus 54 plus 61 divided by five, which is equal to 60. And now we'll do the same thing for why bar, except with, um, the bottom column over here. So 49 plus 21 for 65 plus 47 plus 33 divided by five is equal 2 43 And now we can just plug ah, the values in for the most part. So I'll just give you guys an example of this difference. This difference. And, um, just one of the square differences. So an individual X value minus, the X bar would be equal to 67 minus our exports. 60 67 minus 60 is equal to seven. And now you would take this kind of difference and do it for each of the variables would be 45 minus 60 plus 73 minus 60 54 minus 60 plus 61 minus 60. And then you do that for all of them and then the same thing for the y values. So you take an individual, why value and subtract the mean from it. So our y mean is 43. So 49 minus 43 is equal to six. And now you do this for the rest of the Y values, and then you would plug it into this formula up here. So ultimately, in the end, we will get 624. Do some different color 624 over the sum of our differences and X squared, which is for 80. We get a value of 1.3. So we have our beta one and now we need to come up with a beta subzero. This is the following in the following is the formula for our beta subzero, And that is simply the mean of the wide variable, minus the basis of one value times the mean of the xperia ble. We found the y. I mean to be 43 minus our basis of one which we found to be 1.3 and our ex mean, which is 60. And once we do this, we get a beta subzero value of negative 35. So we get, um, ultimately our estimated regression equation, which is the answer to Part D. That why hat is equal to negative 35 plus 1.3 X. Now, we can use this formula to come up with when, um uh Or what percent of management jobs helped a woman in a company that has 60% of women employees. So what we have to do is just, ah, plug in 60 wherever we see X. And we do that as like we do in this formula over here, and we get a value Ah, 43%


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